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Monthly Archives: March 2011
DMat0101, Notes 5: The Hardy-Littlewood maximal function
1. Averages and maximal operators This week we will be discussing the Hardy-Littlewood maximal function and some closely related maximal type operators. In order to have something concrete let us first of all define the averages of a locally integrable … Continue reading
DMat0101, Notes 4: The Fourier transform of the Schwartz class and tempered distributions
In this section we go back to the space of Schwartz functions and we define the Fourier transform in this set up. This will turn out to be extremely useful and flexible. The reason for this is the fact that … Continue reading
DMat0101, Notes 3: The Fourier transform on L^1
1. Definition and main properties. For , the Fourier transform of is the function Here denotes the inner product of and : Observe that this inner product in is compatible with the Euclidean norm since . It is easy to … Continue reading
Posted in Dmat0101 - Harmonic Analysis, math.CA, Teaching
Tagged Abel summability, approximation to the identity, Fourier Transform, Gauss kernel, Gauss-Weierstrass summability, Harmonic extension, Heat equation, integrable functions, inversion formula, Poisson kernel, Riemann-Lebesgue, summability method
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